title: Direct reconstruction of cardiac PET kinetic parametric images using a preconditioned conjugate gradient approach.
abstract: OBJECTIVE
  Our research goal is to develop an algorithm to reconstruct cardiac positron emission tomography (PET) kinetic parametric images directly from sinograms and compare its performance with the conventional indirect approach.
  
  
  METHODS
  Time activity curves of a NCAT phantom were computed according to a one-tissue compartmental kinetic model with realistic kinetic parameters. The sinograms at each time frame were simulated using the activity distribution for the time frame. The authors reconstructed the parametric images directly from the sinograms by optimizing a cost function, which included the Poisson log-likelihood and a spatial regularization terms, using the preconditioned conjugate gradient (PCG) algorithm with the proposed preconditioner. The proposed preconditioner is a diagonal matrix whose diagonal entries are the ratio of the parameter and the sensitivity of the radioactivity associated with parameter. The authors compared the reconstructed parametric images using the direct approach with those reconstructed using the conventional indirect approach.
  
  
  RESULTS
  At the same bias, the direct approach yielded significant relative reduction in standard deviation by 12%-29% and 32%-70% for 50 × 10(6) and 10 × 10(6) detected coincidences counts, respectively. Also, the PCG method effectively reached a constant value after only 10 iterations (with numerical convergence achieved after 40-50 iterations), while more than 500 iterations were needed for CG.
  
  
  CONCLUSIONS
  The authors have developed a novel approach based on the PCG algorithm to directly reconstruct cardiac PET parametric images from sinograms, and yield better estimation of kinetic parameters than the conventional indirect approach, i.e., curve fitting of reconstructed images. The PCG method increases the convergence rate of reconstruction significantly as compared to the conventional CG method.
authors.affiliation: Center for Advanced Medical Imaging Sciences, Division of Nuclear Medicine and Molecular Imaging, Massachusetts General Hospital, Boston, Massachusetts 02114 and Department of Radiology, Harvard Medical School, Boston, Massachusetts 02114.
authors.forename: Yothin
authors.initials: Y
authors.lastname: Rakvongthai
authors.forename: Jinsong
authors.initials: J
authors.lastname: Ouyang
authors.forename: Bastien
authors.initials: B
authors.lastname: Guerin
authors.forename: Quanzheng
authors.initials: Q
authors.lastname: Li
authors.forename: Nathaniel M
authors.initials: NM
authors.lastname: Alpert
authors.forename: Georges
authors.initials: G
authors.lastname: El Fakhri
mesh_terms: D000465:Algorithms; D006321:Heart / Q000000981:diagnostic imaging*; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D007700:Kinetics; D019047:Phantoms, Imaging; D049268:Positron-Emission Tomography / Q000379:methods*